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Monocular 3D vehicle localization is an important task in Intelligent Transportation System (ITS) and Cooperative Vehicle Infrastructure System (CVIS), which is usually achieved by monocular 3D vehicle detection. However, depth information cannot be obtained directly by monocular cameras due to the inherent imaging mechanism, resulting in more challenging monocular 3D tasks. Most of the current monocular 3D vehicle detection methods leverage 2D detectors and additional geometric modules, which reduces the efficiency. In this paper, we propose a 3D vehicle localization network CenterLoc3D for roadside monocular cameras, which directly predicts centroid and eight vertexes in image space, and the dimension of 3D bounding boxes without 2D detectors. To improve the precision of 3D vehicle localization, we propose a weighted-fusion module and a loss with spatial constraints embedded in CenterLoc3D. Firstly, the transformation matrix between 2D image space and 3D world space is solved by camera calibration. Secondly, vehicle type, centroid, eight vertexes, and the dimension of 3D vehicle bounding boxes are obtained by CenterLoc3D. Finally, centroid in 3D world space can be obtained by camera calibration and CenterLoc3D for 3D vehicle localization. To the best of our knowledge, this is the first application of 3D vehicle localization for roadside monocular cameras. Hence, we also propose a benchmark for this application including a dataset (SVLD-3D), an annotation tool (LabelImg-3D), and evaluation metrics. Through experimental validation, the proposed method achieves high accuracy and real-time performance. (limited words, please see the article for more details)